Combine the crème fraiche, mayo (if using), tarragon, chives, shallot, celery, sea salt, white pepper, and cayenne in a bowl. Mix to combine.
Heat a griddle pan or skillet over medium heat. Split the brioche rolls in half and brush each cut side with the melted butter. Place the rolls buttered side down and cook until golden brown, 3-5 minutes.
Remove from the heat and set aside. Melt 1 teaspoon of butter in a pan over medium heat. When the butter begins to foam, add lobster and lemon juice. Gently toss around to coat and warm up—no more than 30 seconds. Scoop the lobster out of the pan using a slotted spoon, leaving the juice behind.
Add the warm lobster to the cream mixture and gently mix. Stuff each roll with 1/2 the lobster mixture.